# Triangle A has sides of lengths 32 , 44 , and 64 . Triangle B is similar to triangle A and has a side of length 8 . What are the possible lengths of the other two sides of triangle B?

Feb 18, 2016

Possible length of sides of triangle are (8, 11 and 16), (5.82, 8 and 11.64) and (4, 5.5 and 8).

#### Explanation:

Sides of two similar triangles are proportional to each other.

As triangle A has sides of lengths 32, 44, and 64 and triangle B is similar to triangle A and has a side of length 8, the latter could be proportional to 32, 44 or 64.

If it is proportional to 32, other two sides could be $8 \cdot \frac{44}{32} = 11$ and $8 \cdot \frac{64}{32} = 16$ and three sides would be 8, 11 and 16.

If it is proportional to 44, other two sides could be $8 \cdot \frac{32}{44} = 5.82$ and $8 \cdot \frac{64}{44} = 11.64$ and three side would be 5.82, 8 and 11.64.

If it is proportional to 64, other two sides could be $8 \cdot \frac{32}{64} = 4$ and $8 \cdot \frac{44}{64} = 5.5$ and three sides would be 4, 5.5 and 8.